Fluctuation effects at the onset of $\bf 2k_F$ density wave order with one pair of hot spots in two-dimensional metals

TL;DR

This paper investigates quantum fluctuation effects at the onset of $2k_F$ density wave order in 2D metals, revealing non-Fermi liquid behavior, Fermi surface flattening, and conditions for the stability of density wave quantum critical points.

Contribution

It provides a leading-order analysis of fluctuation effects near $2k_F$ density wave onset, highlighting non-Fermi liquid behavior and the impact of self-energy corrections on density wave stability.

Findings

Non-Fermi liquid frequency scaling with vanishing quasiparticle weight.

Divergent renormalization of Fermi velocity and Fermi surface flattening.

One-loop results are not self-consistent, affecting density wave mechanisms.

Abstract

We analyze quantum fluctuation effects at the onset of charge or spin density wave order in two-dimensional metals with an incommensurate $2k_F$ wave vector connecting a single pair of hot spots on the Fermi surface. We compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a fluctuation expansion (one loop). Non-Fermi liquid behavior with anomalous frequency scaling and a vanishing quasi particle weight is obtained. The momentum dependence yields a divergent renormalization of the Fermi velocity and a flattening of the Fermi surface near the hot spots. Going beyond the leading order calculation we find that the one-loop result is not self-consistent. We show that any momentum-independent self-energy with a non-Fermi liquid frequency exponent wipes out the peak of the polarization function at the $2k_F$ wave vector, and thus destroys the mechanism favoring $2k_F$ density waves over those with generic wave vectors. However, a $2k_F$ density wave quantum critical point might survive in presence of a sufficiently flat renormalized Fermi surface.